The present invention relates to a method and apparatus for determining the relative permeability of porous solids.
Relative permeability may be thought of as a useful measure of the effective hydraulic conductivity of a fluid in multiphase flow of immiscible fluid mixtures through interstitial (pore) spaces of porous solids. Each fluid phase has its own relative permeability transport coefficient. These transport coefficients depend on many factors such as whether the particular fluid is wetting or nonwetting with respect to the particular porous solid, the saturation level of the fluid in the body, the partitioning of the pore space among fluids in multiphase flow, and the pore space geometry.
Relative permeability data are important in many areas. For example, relative permeability is extremely important in determining the parameters used in computer simulation of oil recovery systems and in the geochemical field generally.
In a porous body, capillary attraction is a function of the forces of adhesion between a liquid and a solid, and the forces of cohesion of the liquid to itself. A liquid that wets a solid has greater forces of adhesion to the particular solid than does a non-wetting fluid. A fluid may wet one solid and not another solid. A particular fluid may also be wetting or nonwetting in relation to other fluids when considering a single solid. Thus, in multiphase flow, if the force of adhesion of a first fluid for a porous body is greater than the force of adhesion of a second fluid for a porous body, then the first fluid will be considered a wetting fluid for a porous body in relation to the second fluid, even though the force of adhesion for the solid in the first fluid is not as great as the force of cohesion of that first fluid for itself.
The saturation level of a given liquid in a porous body, S, is a value between 0 and 1 that shows the fraction of the available pore space occupied by a particular fluid under consideration. A saturation level of 1 indicates that in a given porous body the entire available pore space is filled by the fluid under consideration. Both a local saturation level within a pore and an overall saturation level within a porous body may be relevant variables.
In a porous body containing two or more immiscible fluids, the local pore space may be partitioned among these fluids differently at each saturation level. For example, one fluid may adhere strongly to the surfaces within a given pore while another may have no effective contact with the solid material. Moreover, the local pore space geometry may vary dramatically within a given porous body.
Of the several relative permeability measurement schemes that have been described in the literature, U.S. Pat. No. 2,345,935 to Hassler is, conceptually at least, superior to other proposed methods, for example U.S. Pat. No. 2,390,252 to Hayward. Unfortunately, however, Hassler's method has many operating difficulties. Most importantly, the Hassler technique involves determination of internal wetting fluid pressures within the porous body. See, e.g., W. Rose, "Some Problems in Applying the Hassler Relative Permeability Method," 32 J. Petroleum Technology, 1161-63 (July, 1980).